Derivation of Einstein Field Equations for a Static, Spherically Symmetric Spacetime

The standard ΛCDM model of cosmology, while remarkably successful in explaining a wide range of observations, faces significant challenges. The Time Field Hypothesis (TFH) proposes an alternative paradigm: a static, infinite, homogeneous universe where cosmic redshift arises from cumulative grav- itational effects. To explore the mathematical viability of TFH within General Relativity (GR), we formulate the Einstein Field Equations (EFE) for a static, spherically symmetric spacetime containing a homogeneous matter distribution and a cosmological constant. This document presents the rigorous derivation of these field equations, which form the fundamental framework for the TFH model.